Associative

A property of binary operations: an associativeoperation does not depend on the order in which operations are performed, so we may dispense with brackets and not have ambiguity. The operation @ is associative if for all x, y and z (in the space on which @ operates), x@(y@z) = (x@y)@z. This is different from being commutative! For instance, if we define the "leftmost" operator x@y=x, we get an operation which is associative, but not commutative.